Abstract
Collaborative Robots (cobots) are devices designed for direct interaction with human operators in a shared workspace. In such devices, the human provides the necessary force for the movement of the system, while the cobot provides a virtual guiding surface. The main purpose of the virtual guiding surfaces is to direct the movement performed by the human such that a desired path can be followed. This work presents simulation results of a planar 2-DOF cobot with differential gears modelled as a differential algebraic system, that is, the well known dynamic model of a planar 2-DOF robot is subject to the algebraic constraint imposed by the velocities that exist on the differential gear train. Moreover, the force exerted by the human operator is decomposed into its cartesian components and modelled as a PD controller.
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References
Colgate JE, Peshkin MA, Wannasuphoprasit W (1996) Nonholonomic haptic display. In: IEEE international conference on robotics and automation, pp 539–544
Peshkin MA, Wannasuphoprasit W, Akella P, Colgate JE (2000) Cobots in material handling. Northwestern University, Evanston
Mustafa S, Marić B (2011) Assisting manual welding with robot. Robot Comput Integr Manuf 27:818–828
Pan P, Lynch K, Peshkin M, Colgate E (2005) Human interaction with passive assistive robots. In: 9th International conference on rehabilitation robotics, 2005
Worsnopp T, Peshkin M, Lynch K, Colgate E (2006) Controlling the apparent inertia of passive human-interactive robots. J Dyn Syst Meas Control 128 (1):44–52
Brenan KE, Campbell SL, Petzold L (1989) Numerical solution of initial-value problems in differential-algebraic equations. Classics in applied mathematics, North-Holland, New York
Costa-Casteló R, Grió R, Basañez L (1998) DAE methods in constrained robotics system simulation Computación y Sistemas, vol 1, pp 145–160, Mexico
Moore CA, Peshkin MA, Colgate JE (1999) Design of a 3R cobot using continuously variable transmissions. In IEEE International Conference on Robotics and Automation (ICRA), 1999
Wannasuphoprasit W, Akella P, Peshkin MA, Colgate JE (1998) Cobots: a novel material handling technology. ASME 98-WA/MH-2
Gellispie R, Peshkin MA, Colgate JE (2001) A general framework for Cobot control. IEEE Trans Robot Autom 17(4):391–401
Peshkin M, Colgate E, Wannasuphoprasit W, Moore C, Gillespie B, Akella P (2001) Cobot architecture. IEEE Trans Robot Autom 17(4):377–390
Dong Y, Zhang L, Dunmin L, Bernhardt R, Surdilovic D (2004) A novel cobot and control. In: Proceedings of the 5th world congress on intelligent control and automation, China
Surdilovic D, Bernhardt L, Zhang L (2003) New intelligent power assist systems based on differential transmission. Robotica 21:295–302
Zhang L, Lu D, Wang L, Shen J, Bernhardt R (2003) Dynamics of five-bar COBOT ussing differential mechanism. J Mar Sci Appl 2(2)
Wannasuphoprasit W, Cillespie RB, Colgate JE, Peshkin MA (1997) Cobot control. In: Proceeding of the IEEE 1997 international conference on robotics and automation
Gear Charles W (1971) Simultaneous numerical solution of differential-algebraic equations. IEEE Trans Circuit Theory CT-18:89–95
Moore C, Peshkin M, Colgate E (2003) Cobot implementation of virtual paths and 3-D virtual surfaces. IEEE Trans Robot Autom 19(2):347–351
Hairer E, Lubich C, Roche M (1989) The numerical solution of differential-algebraic systems by Runge-Kutta methods. Springer, Berlin
Hairer E, Norsett SP, Wanner G (1991) Solving ordinary differential equations. In: Series in Computational Mathemathics, 1991. Springer, Berlin
Ascher UM, Petzold LR (1998) Computer methods for ordinary differential equations and differential-algebraic equations. Society for Industrial and Applied Mathematics (SIAM), Philadelphia
Méndez -Iglesias J, Parra-Vega V, Ruiz-Sánchez F (2005) Identification of the human behavior in virtual environment tasks as a non-linear control block. In: Proceedings of the 16th IFAC world congress, 2005
Gomez C, Bunks C, Chancellier J (1999) Engineering and scientific computing with Scilab. Springer Science + Business Media, New York
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Mendoza-Trejo, O., Cruz-Villar, C.A. (2015). A Planar Cobot Modelled as a Differential Algebraic System. In: Ceccarelli, M., Hernández Martinez, E. (eds) Multibody Mechatronic Systems. Mechanisms and Machine Science, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-09858-6_52
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DOI: https://doi.org/10.1007/978-3-319-09858-6_52
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